# areIsomorphic -- checks if two vector bundles are isomorphic

## Synopsis

• Usage:
b = areIsomorphic(E,F)
• Inputs:
• Outputs:
• b, , whether E and F are isomorphic

## Description

E and F must be vector bundles over the same fan. Two equivariant vector bundles in Klyachko's description are isomorphic if there exists a simultaneous isomorphism for the filtered vector spaces of all rays. The method then returns whether the bundles are isomorphic.

 i1 : HF = hirzebruchFan 2 o1 = HF o1 : Fan i2 : E = exteriorPower(2, cotangentBundle HF) o2 = {dimension of the variety => 2 } number of affine charts => 4 number of rays => 4 rank of the vector bundle => 1 o2 : ToricVectorBundleKlyachko i3 : F = weilToCartier({-1,-1,-1,-1},HF) o3 = {dimension of the variety => 2 } number of affine charts => 4 number of rays => 4 rank of the vector bundle => 1 o3 : ToricVectorBundleKlyachko i4 : areIsomorphic(E,F) o4 = true

To obtain the isomorphism, if two bundles are isomorphic use isomorphism.